Finite Group Databasebeta

← #26233035

Subgroups — #26233035

Order 12032.

1172 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689819C211yesmaximal, characteristic
2#20246267C212yesmaximal, complemented
3#20244223C212yesmaximal, complemented
4#20244222C214yesmaximal, complemented
5#20243375C212yesmaximal, complemented
6C4×#13093939C211yesmaximal, characteristic, complemented
7#20243175C212yesmaximal, complemented
8C47×#1799C211yesmaximal, characteristic, complemented
9#15689819—22no—
10#15689819—24no—
11#15689819—22no—
12C2×#13094019C412yescomplemented
13C2×#13094016C411yescharacteristic, complemented
14C2×#13094006C412yescomplemented
15C2×#13093998C411yescharacteristic, complemented
16C2×#13093998C2211yescharacteristic
17C2×#13093996C2212yes—
18C2×C4×D188C411yescharacteristic, complemented
19C2×(C22⋊D47)⋊C4C2212yes—
20C2×#13093983C411yescharacteristic, complemented
21C22×C4⋊Dic47C2211yescharacteristic
22C2×#13093939C2212yes—
23C2×#13093938C2214yes—
24C2×#13093938C2214yes—
25#15689019—22no—
26#15689008—24no—
27#15688981C2214yes—
28C4⋊C4×Dic47—22no—
29C22⋊C4×Dic47C2214yes—
30C4×C22⋊Dic47C2212yes—
31#15688890C2211yescharacteristic
32#15688890C2211yescharacteristic
33C2×C4×D4×C47C2211yescharacteristic
34C2×#99×C47C2212yes—
35C47×#380C2212yes—
36C47×#342C2212yes—
37C22×D188C2×C411yescharacteristic
38C22×C22⋊D47C2×C412yes—
39C22×C22⋊D47C2312yes—
40C23×Dic47C2312yes—
41C22×C4×D47C2×C412yes—
42#13094019—24no—
43#13094019—24no—
44#13094016—22no—
45#13094016—22no—
46#13094006—24no—
47#13094006—24no—
48#13093998—22no—
49#13093998—22no—
50#13093998—22no—
51#13093998—22no—
52#13093996—24no—
53#13093996—24no—
54C4×D188—22no—
55C4×D188—21no—
56C4×D188—21no—
57(C22⋊D47)⋊C4—24no—
58(C22⋊D47)⋊C4—24no—
59#13093983—22no—
60#13093983—21no—
61#13093983—21no—
62C2×C4⋊Dic47C2×C411yescharacteristic
63C2×C4⋊Dic47C2×C411yescharacteristic
64C2×C4⋊Dic47C2×C411yescharacteristic
65C2×C4⋊Dic47C2×C412yes—
66C2×C4⋊Dic47D412yes—
67C2×C4⋊Dic47D414yes—
68C2×C4⋊Dic47D412yes—
69C2×Dic47⋊C4—24no—
70C2×Dic47⋊C4C2×C412yes—
71C2×Dic47⋊C4C2×C412yes—
72C2×C22⋊Dic47C2×C412yes—
73C2×C22⋊Dic47C2312yes—
74C2×C22⋊Dic47C2312yes—
75C2×(C2×D47)⋊C4C2×C412yes—
76C2×(C2×D47)⋊C4C2×C412yes—
77C2×(C2×D47)⋊C4C2×C412yes—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47C2×C412yes—
81#13093939—24no—
82#13093938—28no—
83#13093938—44no—
84C47⋊#95—22no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C22×D4×C47C2311yescharacteristic
88C23×C4×C47C2×C411yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C4×D4×C47—22no—
91C4×D4×C47—22no—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47C2×C411yescharacteristic
94C2×C22⋊C4×C47C2×C411yescharacteristic
95C2×C22⋊C4×C47C2314yes—
96C2×C22⋊C4×C47C2311yescharacteristic
97C2×C42×C47C2×C411yescharacteristic
98#99×C47—42no—
99#95×C47—22no—
100C24×C47C22×C411yescharacteristic
101C24×C47C2411yescharacteristic
102C23×D47C22×C412yes—
103C2×D4×C47—22no—
104C2×D4×C47—22no—
105C2×D4×C47—21no—
106C2×D4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—24no—
110C22×C4×C47—42no—
111C22×C4×C47—42no—
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C22×C411yescharacteristic
114C22×C4×C47C22×C411yescharacteristic
115C22×C4×C47C22×C411yescharacteristic
116C22×C4×C47C22×C411yescharacteristic
117C22×C4×C47C2×D412yes—
118C22×C4×C47C2×D412yes—
119C2×C22⋊D47—24no—
120C2×C22⋊D47—24no—
121C2×C22⋊D47—22no—
122C2×C22⋊D47—22no—
123C2×C22⋊D47—24no—
124C2×C22⋊D47—82no—
125C22×Dic47—22no—
126C22×Dic47—22no—
127C22×Dic47—82no—
128C22×Dic47C22×C412yes—
129C22×Dic47C22×C412yes—
130C22×Dic47C22×C412yes—
131C22×Dic47C2×D414yes—
132C22×Dic47C2×D414yes—
133C2×D188—21no—
134C2×D188—21no—
135C2×D188—42no—
136C2×C4×D47—22no—
137C2×C4×D47—22no—
138C2×C4×D47—82no—
139C4⋊C4×C47—22no—
140C4⋊C4×C47—44no—
141C22⋊C4×C47—22no—
142C22⋊C4×C47—22no—
143C22⋊C4×C47—24no—
144C22⋊C4×C47—24no—
145C42×C47—21no—
146C42×C47—21no—
147C22⋊Dic47—22no—
148C22⋊Dic47—22no—
149C22⋊Dic47—22no—
150C22⋊Dic47—22no—
151C22⋊Dic47—22no—
152C22⋊Dic47#4114yes—
153(C2×D47)⋊C4—24no—
154(C2×D47)⋊C4—24no—
155(C2×D47)⋊C4—22no—
156(C2×D47)⋊C4—22no—
157C4⋊Dic47—21no—
158C4⋊Dic47—21no—
159C4⋊Dic47C22⋊C412yes—
160C4⋊Dic47C22⋊C411yescharacteristic
161C4⋊Dic47C22⋊C411yescharacteristic
162C4⋊Dic47C22⋊C412yes—
163C4⋊Dic47C22⋊C412yes—
164C4⋊Dic47C22⋊C414yes—
165C4⋊Dic47C22⋊C414yes—
166Dic47⋊C4—24no—
167Dic47⋊C4—24no—
168Dic47⋊C4—84no—
169C4×Dic47—22no—
170C4×Dic47—22no—
171C4×Dic47—44no—
172C4×Dic47—84no—
173C23×C47—21no—
174C23×C47—21no—
175C23×C47—21no—
176C23×C47—41no—
177C23×C47—41no—
178C23×C47—41no—
179C23×C47—41no—
180C23×C47C23×C411yescharacteristic
181C23×C47C22×D412yes—
182C23×C47C2×#4112yes—
183C23×C47H(5,𝔽2)11yescharacteristic
184C23×C472−1+411yescharacteristic
185C22×D47—22no—
186C22×D47—22no—
187C22×D47—22no—
188C22×D47—42no—
189C22×D47—42no—
190D4×C47—42no—
191D4×C47—42no—
192C2×C4×C47—24no—
193C2×C4×C47—22no—
194C2×C4×C47—21no—
195C2×C4×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—21no—
199C2×C4×C47—41no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—44no—
206C2×C4×C47—44no—
207C2×C4×C47—44no—
208C2×C4×C47C2×C22⋊C411yescharacteristic
209C2×C4×C47C2×C22⋊C412yes—
210C2×C4×C47C2×C22⋊C411yescharacteristic
211C22⋊D47—44no—
212C22⋊D47—44no—
213C22⋊D47—84no—
214C2×Dic47—22no—
215C2×Dic47—22no—
216C2×Dic47—22no—
217C2×Dic47—24no—
218C2×Dic47—44no—
219C2×Dic47—44no—
220C2×Dic47—42no—
221C2×Dic47—42no—
222C2×Dic47—42no—
223C2×Dic47—42no—
224C2×Dic47—42no—
225C2×Dic47—42no—
226C2×Dic47—42no—
227C2×Dic47C2×C22⋊C412yes—
228C2×Dic47C2×C22⋊C412yes—
229C2×Dic47C2×C22⋊C414yes—
230D188—42no—
231D188—42no—
232C4×D47—82no—
233C4×D47—82no—
234#22535—471nomaximal, Sylow
235C22×C47—22no—
236C22×C47—21no—
237C22×C47—22no—
238C22×C47—21no—
239C22×C47—42no—
240C22×C47—41no—
241C22×C47—41no—
242C22×C47—41no—
243C22×C47—41no—
244C22×C47—41no—
245C22×C47—81no—
246C22×C47—81no—
247C22×C47C22×C22⋊C411yescharacteristic
248C22×C47C4×#4111yescharacteristic
249C22×C47#52011yescharacteristic
250C22×C47#54812yes—
251C22×C47#55012yes—
252C2×D47—42no—
253C2×D47—42no—
254C2×D47—42no—
255C2×D47—82no—
256C2×D47—82no—
257C4×C47—21no—
258C4×C47—22no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—84no—
263C4×C47#41012yes—
264Dic47—22no—
265Dic47—22no—
266Dic47—24no—
267Dic47—44no—
268Dic47—42no—
269Dic47—82no—
270C2×#553—471no—
271#2345—472no—
272#1964—474no—
273#1964—472no—
274#1799—472no—
275#1799D4711yescharacteristic, complemented
276C4×#99—472no—
277C4×#99—471no—
278C2×C47—22no—
279C2×C47—22no—
280C2×C47—21no—
281C2×C47—21no—
282C2×C47—81no—
283C2×C47#234111yescharacteristic
284C2×C47C2×#41011yescharacteristic
285C2×C47#288311yescharacteristic
286D47—82no—
287#553—942no—
288#553—944no—
289#553—942no—
290C2×#126—472no—
291C2×#125—471no—
292C2×#123—472no—
293C2×#121—472no—
294C2×#121—471no—
295C2×#121—471no—
296C2×C4×D4—472no—
297C2×C4×D4—471no—
298C2×C4×D4C2×D4711yescharacteristic
299C2×#117—471no—
300C22×C4⋊C4—471no—
301C2×#99—472no—
302C2×#99—474no—
303C2×#99—474no—
304C2×#99C2×D4712yes—
305#389—942no—
306#387—944no—
307#380—474no—
308#380C2×D4712yes—
309C4×C4⋊C4—942no—
310C4×C22⋊C4—472no—
311C4×C22⋊C4—474no—
312#342—471no—
313#342—471no—
314#342C2×D4712yes—
315C47#2253511yescharacteristic, complemented, Sylow
316C22×D4—472no—
317C22×D4—472no—
318C22×D4—471no—
319C22×D4C22×D4711yescharacteristic
320C23×C4—472no—
321C23×C4—472no—
322C23×C4C4×D4711yescharacteristic
323C23×C4C22×D4711yescharacteristic
324#126—944no—
325#126—944no—
326#125—942no—
327#125—942no—
328#123—944no—
329#123—944no—
330#121—942no—
331#121—942no—
332#121—944no—
333#121—944no—
334#121—942no—
335#121—942no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—942no—
339C4×D4—941no—
340C4×D4—941no—
341C4×D4—944no—
342C4×D4—944no—
343#117—942no—
344#117—941no—
345#117—941no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—471no—
348C2×C4⋊C4—471no—
349C2×C4⋊C4—472no—
350C2×C4⋊C4—472no—
351C2×C4⋊C4—474no—
352C2×C4⋊C4—472no—
353C2×C4⋊C4—471no—
354C2×C4⋊C4—472no—
355C2×C4⋊C4—472no—
356C2×C4⋊C4—944no—
357C2×C4⋊C4C4×D4711yescharacteristic
358C2×C22⋊C4—472no—
359C2×C22⋊C4—472no—
360C2×C22⋊C4—472no—
361C2×C22⋊C4—472no—
362C2×C22⋊C4—472no—
363C2×C22⋊C4—472no—
364C2×C22⋊C4C4×D4711yescharacteristic
365C2×C22⋊C4C22×D4714yes—
366C2×C22⋊C4C22×D4711yescharacteristic
367C2×C42—472no—
368C2×C42—944no—
369C2×C42—942no—
370C2×C42C4×D4711yescharacteristic
371#99—42no—
372#99—948no—
373#99—944no—
374#99—1884no—
375#95—22no—
376#95—944no—
377#95—944no—
378#95—942no—
379C24—472no—
380C24C2×C4×D4711yescharacteristic
381C24C23×D4711yescharacteristic
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—944no—
387C2×D4—944no—
388C2×D4—944no—
389C2×D4—942no—
390C2×D4—942no—
391C2×D4—941no—
392C2×D4—941no—
393C2×D4—3762no—
394C2×D4—1882no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—24no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—472no—
401C22×C4—472no—
402C22×C4—474no—
403C22×C4—474no—
404C22×C4—472no—
405C22×C4—942no—
406C22×C4—942no—
407C22×C4—942no—
408C22×C4—942no—
409C22×C4—3762no—
410C22×C4—3762no—
411C22×C4C2×C4×D4711yescharacteristic
412C22×C4C2×C4×D4711yescharacteristic
413C22×C4C2×C4×D4711yescharacteristic
414C22×C4C2×C4×D4711yescharacteristic
415C22×C4C2×C4×D4711yescharacteristic
416C22×C4D4×D4712yes—
417C22×C4D4×D4712yes—
418C4⋊C4—22no—
419C4⋊C4—44no—
420C4⋊C4—472no—
421C4⋊C4—471no—
422C4⋊C4—471no—
423C4⋊C4—472no—
424C4⋊C4—472no—
425C4⋊C4—474no—
426C4⋊C4—474no—
427C4⋊C4—944no—
428C4⋊C4—944no—
429C4⋊C4—941no—
430C4⋊C4—941no—
431C4⋊C4—3764no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—474no—
437C22⋊C4—942no—
438C22⋊C4—942no—
439C22⋊C4—944no—
440C22⋊C4—942no—
441C22⋊C4—942no—
442C22⋊C4—942no—
443C22⋊C4—944no—
444C22⋊C4—942no—
445C22⋊C4—942no—
446C42—21no—
447C42—21no—
448C42—942no—
449C42—942no—
450C42—3764no—
451C42—1884no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—942no—
460C23—942no—
461C23—942no—
462C23—1882no—
463C23—1882no—
464C23C22×C4×D4711yescharacteristic
465C23C2×D4×D4712yes—
466C23#41×D4712yes—
467C23#1309406911yescharacteristic
468C23#1309407211yescharacteristic
469D4—42no—
470D4—42no—
471D4—3764no—
472D4—1882no—
473D4—1884no—
474D4—1884no—
475D4—1882no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—472no—
493C2×C4—472no—
494C2×C4—474no—
495C2×C4—944no—
496C2×C4—942no—
497C2×C4—942no—
498C2×C4—942no—
499C2×C4—3762no—
500C2×C4—3762no—
501C2×C4—1884no—
502C2×C4—1884no—
503C2×C4—1882no—
504C2×C4—1882no—
505C2×C4—1882no—
506C2×C4—1882no—
507C2×C4—1882no—
508C2×C4—1882no—
509C2×C4—1882no—
510C2×C4C22⋊C4×D4711yescharacteristic
511C2×C4C22⋊C4×D4712yes—
512C2×C4C22⋊C4×D4711yescharacteristic
513C22—22no—
514C22—21no—
515C22—22no—
516C22—21no—
517C22—42no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—81no—
524C22—81no—
525C22—3762no—
526C22—3762no—
527C22—1882no—
528C22—1882no—
529C22—1882no—
530C22C2×C22⋊C4×D4711yescharacteristic
531C22#1568959111yescharacteristic
532C22#1568960411yescharacteristic
533C22#1568978312yes—
534C22#1568979112yes—
535C4—21no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—84no—
541C4—942no—
542C4—942no—
543C4—944no—
544C4—3762no—
545C4—1884no—
546C4—1882no—
547C4#1568909512yes—
548C2—22no—
549C2—22no—
550C2—21no—
551C2—21no—
552C2—81no—
553C2—3762no—
554C2#2024622511yescharacteristic
555C2C2×#1568909511yescharacteristic
556C2#2025184711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1799C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689819C2
cosocleC24×C47C24
hypercenter#1799D47
hypocenterC47#22535
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20246267C2semidirect
3. #20244223C2semidirect
4. #20244222C2semidirect
5. #20243375C2semidirect
6. C4×#13093939C2semidirect
7. #20243175C2semidirect
8. C47×#1799C2semidirect
12. C2×#13094019C4semidirect
13. C2×#13094016C4semidirect
14. C2×#13094006C4semidirect
15. C2×#13093998C4semidirect
18. C2×C4×D188C4semidirect
20. C2×#13093983C4semidirect
275. #1799D47semidirect
315. C47#22535semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156898192
#202462672
#202442232
#202442222
#202433752
C4×#130939392
#202431752
C47×#17992
#2253547